Incident Rays Research Articles

Investigation on underwater positioning stochastic model based on acoustic ray incidence angle

High-precision underwater positioning requires more accurate stochastic model. The commonly used equal weight stochastic model (EWSM) cannot be effective in precise underwater positioning process under the assumption of equal-precision observation. In this paper, inaccurate stochastic model effect on the positioning precision is analyzed and a novel acoustic ray incidence angle stochastic model (IASM) is proposed by taking the ranging error and the uncorrected acoustic ray bending error into consideration to improve positioning accuracy. The performance of both EWSM and IASM involving four different forms (the general proportional form, the cosine form, the exponent form and the piecewise cosine form) is tested by the simulation and experiment. The simulation results show that positioning accuracy for underwater static objects is 0.386 m when adopting EWSM while positioning accuracy is 0.334 m, 0.196 m, 0.318 m and 0.091 m when adopting four forms of IASM respectively and sequentially. The experiment results show that the positioning accuracy can be superiorly improved from 1.187 m in EWSM scheme to 0.991 m based on IASM in piecewise cosine form. It’s obvious that the novel IASM can perform better than conventional EWSM in terms of positioning accuracy according to testing results.

Deformaciones de haces cilíndricos y cónicos al atravesar una placa plano-paralela de cristal uniaxial

Una de las herramientas más usadas en la óptica es el trazado de rayos ya que es la herramienta fundamental para el diseño de todo instrumento óptico. En este trabajo se analizan las sucesivas deformaciones que un haz cilíndrico (modelo a primer orden de un haz colimado) y un haz cónico (modelo a primer orden de un haz divergente o convergente), que inciden normalmente sobre una placa planoparalela de cristal uniaxial, sufren a medida que van atravesando las distintas interfaces. Esto se hace siguiendo el camino de cada rayo incidente sobre la primera interfaz. El trazado de rayos para los rayos ordinarios es igual al trazado de rayos en medios isótropos. El trazado de rayos extraordinario, en cambio, presenta más dificultad ya que los rayos no están contenidos en el plano de incidencia y no coinciden con las normales a los frentes de onda. Se analizan también la pérdida de simetría de revolución de los haces y la formación de las sucesivas imágenes.

Design for segmented optical antenna with hexagon-shaped spherical sub-mirrors based on three-dimensional vector rotation and reflection theories

Segmented antenna is an effective method to cut costs of the large-aperture optical antenna. A 10 m-aperture segmented antenna model is established by using three-dimensional (3-D) vector rotation theory. Ray tracing and transmission characteristic analysis are performed based on 3-D vector reflection theory. The receiving efficiency of the segmented antenna composed of 36 spherical sub-mirrors is 80.19%. Results of the optical aberrations caused by tilt ray incidence and defocusing of the secondary reflector indicate that the performance of the proposed segmented antenna with spherical sub-mirrors is very approximate to that of the segmented antenna with paraboloidal sub-mirrors, and hence of great significance for realization of large-aperture optical antenna.

Influence of helix twisted tape on heat transfer and friction factor in forced circulation V-trough solar water heater

ABSTRACTThe effect of helix twisted tape with several twist ratios (Y = 3, 4, 5 and 6) in a V-trough solar water heater for enhancing heat transfer, thermal performance and the friction factor has been examined experimentally in forced circulation with the Reynolds number ranging from 3000 to 23,000. The experimental results of plain V-trough solar collector (PVT) fitted with the standard equations and the variation in the Nusselt number are ±7.23% and the variation in friction factor is about ±5.91%. The PVT has been compared with plain flat plate (PFP) collector. The obtained result shows that the average Nusselt number of PVT performs better than PFP by 8.4%. This is owing to the additional reflectors, reflection of the solar incident rays to the receiver plate, which tend to rise in the temperature gradient of water inlet and outlet of the system. The thermal performance has been increased further by inserting the helix twisted tape with several twist ratios and the results are also presented. The minimum twist ratio 3 provides a higher heat transfer rate and friction factor owing to the increase in the hydraulic length and swirl flow. The experimental Nusselt number and friction factor are correlated and the deficiency falls ±6.44% and ±11.91%, respectively.

Radiative albedo from a linearly fibered half-space

.A growing acceptance of fiber-reinforced composite materials imparts some relevance to exploring the effects which a predominantly linear scattering lattice may have upon interior radiative transport. Indeed, a central feature of electromagnetic wave propagation within such a lattice, if sufficiently dilute, is ray confinement to cones whose half-angles are set by that between lattice and the incident ray. When such propagation is subordinated to a viewpoint of an unpolarized intensity transport, one arrives at a somewhat simplified variant of the Boltzmann equation with spherical scattering demoted to its cylindrical counterpart. With a view to initiating a hopefully wider discussion of such phenomena, we follow through in detail the half-space albedo problem. This is done first along canonical lines that harness the Wiener-Hopf technique, and then once more in a discrete ordinates setting via flux decomposition along the eigenbasis of the underlying attenuation/scattering matrix. Good agreement is seen to prevail. We further suggest that the Case singular eigenfunction apparatus could likewise be evolved here in close analogy to its original, spherical scattering model. A cursory contact with related problems in the astrophysical literature suggests, in addition, that the basic physical fidelity of our scalar radiative transfer equation (RTE) remains open to improvement by passage to a (4×1) Stokes vector, (4×4) matricial setting.

Study on Dynamic Development of Three-dimensional Weld Pool Surface in Stationary GTAW

AbstractThe weld pool contains abundant information about the welding process. In particular, the type of the weld pool surface shape, i. e., convex or concave, is determined by the weld penetration. To detect it, an innovative laser-vision-based sensing method is employed to observe the weld pool surface of the gas tungsten arc welding (GTAW). A low-power laser dots pattern is projected onto the entire weld pool surface. Its reflection is intercepted by a screen and captured by a camera. Then the dynamic development process of the weld pool surface can be detected. By observing and analyzing, the change of the reflected laser dots reflection pattern, for shape of the weld pool surface shape, was found to closely correlate to the penetration of weld pool in the welding process. A mathematical model was proposed to correlate the incident ray, reflected ray, screen and surface of weld pool based on structured laser specular reflection. The dynamic variation of the weld pool surface and its corresponding dots laser pattern were simulated and analyzed. By combining the experimental data and the mathematical analysis, the results show that the pattern of the reflected laser dots pattern is closely correlated to the development of weld pool, such as the weld penetration. The concavity of the pool surface was found to increase rapidly after the surface shape was changed from convex to concave during the stationary GTAW process.

Conductive and transparent submicron polymer lens array fabrication for electrowetting applications

In this study, we have demonstrated a simple and inexpensive process to fabricate electrowetting lens arrays with various curvatures (micron to submicron) on conductive and transparent polydimethylsiloxane (PDMS) molds without additional metal layers. The microlens arrays were fabricated using one-step dual diffuser lithography process, which utilizes a pair of diffusers to diffract the incident rays of UV light at wide angles before approaching the photoresist. Dimensional control and high fill factor was achieved by just varying the exposure energy and gap between the patterns in the photomask, respectively. The patterns were replicated in conductive and transparent Ag(n)-PDMS (5–20% Ag) with 15 μm thickness. High conductivity of 4.6 × 10−1 S/m and high transmission efficiency of 90% was demonstrated by Ag(n)-PDMS molds. Micro-nanolens arrays fabricated by the optimized corelation were utilized to demonstrate switchable wettability behavior of water droplet at different applied voltages. The electrowetting microlens array fabrication method introduced in this work has high potential to be incorporated in optoelectronics and biomedical devices.

17.1: Invited Paper: Optical interaction enabled by sub‐wavelength metamaterials: fabrication process and system demos

Human‐machine interaction is the inevitable medium for people to obtain information from display devices. The evaluation of interaction technologies consist one of the most important parts of the rapid development of display industry. Fifty years ago, mouse and keyboard had brought about great convenience for people to operate machines, while the transparent capacitive touching technology led by Apple's ‘Iphone’ 10 years ago, revolutionarily enable people to use fingers‐the native and ultimate locating ‘device’ to touch and operate the displays.Until now, most of the ‘touching’ technologies only work on the plane dimensional of screens. While, in this talk, we will show a novel optical touching technology based on sub‐wavelength meta‐materials which cover the incident rays into wave guided light for position detection and interaction. By using roll‐to‐roll nano‐imprinting, larger scale fabrication of the sub‐wavelength optical films have been fulfilled and a prototype of optical touch screen has been made, paving the way to mass commercialization.

The differential equation of an arbitrary reflecting surface

A differential equation describing the reflection of a light ray incident upon an arbitrary reflecting surface is obtained using the law of reflection. The derived equation is written in terms of a parameter and the value of this parameter determines the nature of the reflecting surface. Under various parametric constraints, the solution of the differential equation leads to the various conic surfaces but is not generally solvable. In addition, the dynamics of the light reflections from the conic surfaces are executed in the Mathematica software. Our derivation is the converse of the traditional approach and our analysis assumes a relation between the object distance and the image distance. This leads to the differential equation of the reflecting surface.

A shooting direction control camera based on computational imaging without mechanical motion

To take an image of object at long distance, a camera which has long-focus lens is used. However, if the focal length is long, the field of shooting becomes narrowed. Therefore, the shooting direction of the camera must be controlled. Recently, pan/tilt camera, whose direction is driven mechanically, has been used for surveillance. However, it is difficult to control quickly for long-focus camera because of weight of lens. We proposed a camera which has controllability of shooting direction without mechanical motion and high-resolution image of distant object based on computational imaging. The proposed camera is composed of ray-direction limiting optics and lens array. The direction of incident rays are limited and determined by the position of the aperture in the raydirection limiting optics, it is possible to control the shooting direction without mechanical motion. By using a lens array, a number of small optical images are formed on most area of the image sensor and digitized. Each digitized image is low-resolution because of small size. To reconstruct high-resolution image from low-resolution images, we adopted reconstruction-based super resolution technique. We did simulation under realistic conditions and confirmed the principle of the proposed camera.

Feedback control of a tower solar plant with an optical corner reflector

Abstract In a thermal solar power tower plant, a field of heliostats reflects the solar radiation onto a receiver placed at the top of a tower. The heliostats must be appropriately positioned according to the sun position; this is usually done in open loop by exploiting the ephemeris data. In this paper we propose a closed-loop control where feedback is achieved with a corner reflector. This optical component, positioned at the centre of the receiver, has the distinctive feature of reflecting an incident ray in the same direction. Hence, the heliostat is correctly positioned only when the reflected sun light ray, further reflected by the corner reflector, hits its centre. The occurrence of this can be tested with a camera located close to the heliostat, suitable oriented towards the corner reflector.

A new approach for direct imaging of Alpha radiation by using Micro Pattern Gas Detectors in SQS mode

In this study, the design, simulation and construction of three micro pattern gas-detectors, THGEM, with different geometric dimensions are presented. Moreover, their ability of operation in SQS mode to determine the incident rays position without using any conventional imaging system is investigated. In the presence of UV absorbing gas mixtures, the proportional mode of the gas detector operation is followed by SQS mode as soon as the visible light column appears at the ray entrance location. In the method employed, each THGEM hole as an image pixel independent of other holes can operate in SQS mode with emerging a light column.As a consequence, it can be used for alpha beam imaging since the brightness of each hole at a certain voltage is proportional to the number of primary electrons entering the hole.

Development of a hemispherical rotational modulation collimator system for imaging spatial distribution of radiation sources

Detecting and mapping the spatial distribution of radioactive materials is of great importance for environmental and security issues. We design and present a novel hemispherical rotational modulation collimator (H-RMC) system which can visualize the location of the radiation source by collecting signals from incident rays that go through collimator masks. The H-RMC system comprises a servo motor-controlled rotating module and a hollow heavy-metallic hemisphere with slits/slats equally spaced with the same angle subtended from the main axis. In addition, we also designed an auxiliary instrument to test the imaging performance of the H-RMC system, comprising a high-precision x- and y-axis staging station on which one can mount radiation sources of various shapes. We fabricated the H-RMC system which can be operated in a fully-automated fashion through the computer-based controller, and verify the accuracy and reproducibility of the system by measuring the rotational and linear positions with respect to the programmed values. Our H-RMC system may provide a pivotal tool for spatial radiation imaging with high reliability and accuracy.

Depth recovering method immune to projector errors in fringe projection profilometry by use of cross-ratio invariance

In fringe projection profilometry, the projector parameters are difficult to calibrate accurately thus inducing errors in measurement results. To solve this problem, this paper analyzes the epipolar geometry of the fringe projection system, revealing that, on an epipolar plane, the depth variation along an incident ray induces the pixel movement along the epipolar line on the image plane of the camera. The depth variation and the pixel movement can be related to each other by using projective transformations. Under this condition, their cross-ratio keeps invariant. By use of this cross-ratio invariance, we suggest a depth recovering method immune to projector errors. To calibrate the measurement system, we shift a reference board perpendicularly to three positions with known depths and measure its phase maps as the reference phase maps. When measuring an object, we calculate the object depth at each pixel by equating the cross-ratio of the depths to that of the corresponding pixels having the same phase. Experimental results demonstrate that, with this technique, the errors associated with the projector, including its errors in geometry parameters, its lens distortions, and its luminance nonlinearity, do not affect the measurement results.

Multi-element direct design using a freeform surface for a compact illumination system.

An iterative optimization algorithm is introduced to address the surface iterative errors as well as source extension issues in a freeform illumination system for producing satisfactory illumination distribution. A unique two-parameter coordinate system is utilized to represent the emitted ray directions. Then, the direction vector for the incident rays, which propagate through several surfaces, is obtained using ray-tracing techniques. Based on the mapping between the incoming rays and a target grid, a freeform surface is generated as a good starting design. An iterative optimization strategy is further employed to alleviate the deterioration of illumination distribution on the target region, and the uniformity of the illumination system is evaluated during optimization. Very few variables are demanded, and more flexibility in the design of the freeform surface is offered. Successive iterations can be performed until the desired result is attained. An optical system is used as an example to demonstrate the validity of the proposed method, and numerical simulations are carried out to evaluate the optical performance. The simulation results show that a small angular intensity distribution and prescribed rectangular illumination pattern can be achieved simultaneously.

Effects of the micro-structure of arc-shaped groove, rectangular groove and semicircle-based rectangular groove on the reflectance of silicon solar cell

Light trapping structure in silicon solar cells can produce multi-reflectance of light and improve light absorption. In order to study the effects of micro-structure with different structure parameters on the reflectance of rays for a wavelength range of 300 nm–1200 nm, a numerical algorithm is utilized to trace the propagation path of rays and Fresnel equations are used, and wavelength and incidence are considered to determine the reflectance of every single ray at each reflection point. The weighted reflectance defined as ultimate reflectance for the whole rays projects onto silicon cell is calculated and the light trapping efficiency of micro-structure is analyzed. For rectangular groove microstructure, the weighted reflectance can reach zero theoretically, When primary incidence (defined as the initial incidence of rays when projecting onto silicon solar cells) θp≥60°, the weighted reflectance is less than 10% for all wavelength rays when rectangular groove structure parameters are in specific range, More intensively, when wavelength of rays are in the range of 400 nm–1200 nm, the reflectance can be smaller than 8% for a refined parameters range.

Using proton radiation from the moon to search for diurnal variation of regolith hydrogenation

With the help of a new observing technique, we have detected diurnal variations in both lunar albedo protons and incident galactic cosmic rays (GCRs) at the Moon. Using the Cosmic Ray Telescope for the Effects of Radiation (CRaTER) instrument on the Lunar Reconnaissance Orbiter (LRO), we have combined specific, targeted observations of the lunar horizon with our nominal nadir-viewing data to find a tentative enhancement in the yield of lunar albedo protons at the local sunrise terminator of the Moon relative to the local sunset terminator. A diurnal variation in hydrogenation in the top few cm of regolith is one possible interpretation of this result. We have also measured an unanticipated AM/PM difference in the arriving GCRs at the Moon which can be explained by a known streaming anisotropy. The relatively small data set used here (compared to previous mapping studies of CRaTER data) and heretofore untried horizon observations required us to develop improved data analysis techniques, which we will use in the future to revisit previous data sets and to analyze planned new horizon observations of lunar albedo protons.

Physical-geometric optics method for large size faceted particles.

A new physical-geometric optics method is developed to compute the single-scattering properties of faceted particles. It incorporates a general absorption vector to accurately account for inhomogeneous wave effects, and subsequently yields the relevant analytical formulas effective and computationally efficient for absorptive scattering particles. A bundle of rays incident on a certain facet can be traced as a single beam. For a beam incident on multiple facets, a systematic beam-splitting technique based on computer graphics is used to split the original beam into several sub-beams so that each sub-beam is incident only on an individual facet. The new beam-splitting technique significantly reduces the computational burden. The present physical-geometric optics method can be generalized to arbitrary faceted particles with either convex or concave shapes and with a homogeneous or an inhomogeneous (e.g., a particle with a core) composition. The single-scattering properties of irregular convex homogeneous and inhomogeneous hexahedra are simulated and compared to their counterparts from two other methods including a numerically rigorous method.

The caustic structure near a grazing point in the plane

A grazing point of a concave mirror illuminated by a large beam of rays is a point of the mirror's edge where the incident ray is parallel to the mirror. In the neighborhood of such point the rays are reflected a great number of times. We show that an ordered series of caustics passes through the grazing point, each caustic corresponding to a fixed number of reflections by the mirror. We study, in the framework of planar geometrical optics, the structure of this remarkable set of caustics. Our main result is a formula giving the curvature of the caustic curves at the grazing point as a function of the number of reflections. This sequence is universal in the sense that it is independent of the shape of the incident wavefront. A grazing point in the plane is an unstable point and we show how the caustic structure is modified under the effect of a small perturbation of the optical system.

The problem of camouflaging via mirror reflections.

This work is related to billiards and their applications in geometric optics. It is known that perfectly invisible bodies with mirror surface do not exist. It is, therefore, natural to search for bodies that are, in a sense, close to invisible. We introduce a visibility index of a body measuring the mean angle of deviation of incident light rays, and derive a lower estimate for this index. This estimate is a function of the body's volume and of the minimal radius of a ball containing the body. This result is far from being final and opens a possibility for further research.